New and possibly interesting features from Julia v1.7

We might want to make some changes in Trixi.jl based on the following new features of Julia v1.7:

- `(; a, b) = x` can now be used to destructure properties `a` and `b` of `x` (https://github.com/JuliaLang/julia/blob/v1.7.0-beta2/NEWS.md#new-language-features)
- New `keepat!(vector, inds)` function which is the inplace equivalent of `vector[inds]` for a list `inds` of integers (https://github.com/JuliaLang/julia/blob/v1.7.0-beta2/NEWS.md#new-library-functions)
- Pasting repl examples into the repl (prompt pasting) now supports all repl modes (`julia`, `pkg`, `shell`, `help?`) and switches mode automatically (https://github.com/JuliaLang/julia/blob/v1.7.0-beta2/NEWS.md#repl)

See https://github.com/trixi-framework/Trixi.jl/pull/665#issuecomment-867478367

We should also move testing etc. to Julia v1.7 and state that only that version is officially supported. Of course, we also need to adapt the compat bounds if we use any of the new features introduced in Julia v1.7.

Start by reviewing the Julia v1.7 language, library, and REPL changes linked in the issue, along with the referenced pull-request comment. Then inspect the testing setup and Julia compatibility bounds; done means the relevant changes are identified, tests target Julia v1.7, official support is stated, and compatibility metadata is updated where needed.

Written by the indexing model from the issue text.